Related papers: A Limit Theorem for Radix Sort and Tries with Mark…
Suffix sort plays a critical role in various computational algorithms including genomics as well as in frequently used day to day software applications. The sorting algorithm becomes tricky when we have lot of repeated characters in the…
The successive discrete structures generated by a sequential algorithm from random input constitute a Markov chain that may exhibit long term dependence on its first few input values. Using examples from random graph theory and search…
Logically constrained rewrite systems (LCTRSs) are a versatile and efficient rewriting formalism that can be used to model programs from various programming paradigms, as well as simplification systems in compilers and SMT solvers. In this…
This paper describes substantial advances in the analysis (parsing) of diagrams using constraint grammars. The addition of set types to the grammar and spatial indexing of the data make it possible to efficiently parse real diagrams of…
Markov chain Monte Carlo (MCMC) sampling of densities restricted to linearly constrained domains is an important task arising in Bayesian treatment of inverse problems in the natural sciences. While efficient algorithms for uniform polytope…
We give an algorithmic-bijective proof of Macdonald's reduced word identity in the theory of Schubert polynomials, in the special case where the permutation is dominant. Our bijection uses a novel application of David Little's generalized…
This paper faces a central theme in applied statistics and information science, which is the assessment of the stochastic structure of rank-size laws in text analysis. We consider the words in a corpus by ranking them on the basis of their…
Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…
This work describes the principled design of a theoretical framework leading to fast and accurate algorithmic information measures on finite multisets of finite strings by means of compression. One distinctive feature of our approach is to…
Dictionary learning is the problem of estimating the collection of atomic elements that provide a sparse representation of measured/collected signals or data. This paper finds fundamental limits on the sample complexity of estimating…
An effective 'on-the-fly' mechanism for stochastic lossy coding of Markov sources using string matching techniques is proposed in this paper. Earlier work has shown that the rate-distortion bound can be asymptotically achieved by a 'natural…
Using multisets, we develop novel techniques for mechanizing the proofs of the synthesis conjectures for list-sorting algorithms, and we demonstrate them in the Theorema system. We use the classical principle of extracting the algorithm as…
It is well known that n integers in the range [1,n^c] can be sorted in O(n) time in the RAM model using radix sorting. More generally, integers in any range [1,U] can be sorted in O(n sqrt{loglog n}) time. However, these algorithms use O(n)…
We study a suffix tree built from a sequence generated by a Markovian source. Such sources are more realistic probabilistic models for text generation, data compression, molecular applications, and so forth. We prove that the average size…
Recent developments in termination analysis for declarative programs emphasize the use of appropriate models for the logical theory representing the program at stake as a generic approach to prove termination of declarative programs. In…
In this master thesis we analyze the complexity of sorting a set of strings. It was shown that the complexity of sorting strings can be naturally expressed in terms of the prefix trie induced by the set of strings. The model of computation…
We propose a new statistical model for computational linguistics. Rather than trying to estimate directly the probability distribution of a random sentence of the language, we define a Markov chain on finite sets of sentences with many…
We study very simple sorting algorithms based on a probabilistic comparator model. In our model, errors in comparing two elements are due to (1) the energy or effort put in the comparison and (2) the difference between the compared…
Contention resolution schemes have proven to be an incredibly powerful concept which allows to tackle a broad class of problems. The framework has been initially designed to handle submodular optimization under various types of constraints,…
Constraint propagation is one of the techniques central to the success of constraint programming. To reduce search, fast algorithms associated with each constraint prune the domains of variables. With global (or non-binary) constraints, the…